Fractional modeling of CD38-mediated multiple myeloma dynamics with immune interaction and therapy effects dynamics

Multiple myeloma is a hematological malignancy characterized by the uncontrolled proliferation of plasma cells within the bone marrow microenvironment. Despite significant progress in immunotherapy, particularly with CD38-targeted monoclonal antibodies, treatment resistance and disease relapse remain major clinical challenges. In this study, we develop a fractional-order mathematical model describing the interactions between healthy marrow cells, CD38-positive malignant plasma cells, and CD38-negative malignant cells associated with therapeutic resistance. The model incorporates immune-mediated tumor suppression and treatment-induced phenotypic switching mechanisms. The principal mathematical contribution is the formulation of a fractional-order CD38-mediated multiple myeloma model that combines immune interactions, therapy-induced phenotypic switching, and memory-dependent dynamics within a unified framework. To capture biological memory effects arising from cumulative therapy exposure and delayed immune responses, the system is formulated using the Caputo fractional derivative. The qualitative properties of the model are rigorously investigated. We establish the existence, uniqueness, positivity, and boundedness of solutions, ensuring biological feasibility of the system. A threshold quantity representing the effective reproductive capacity of malignant cells is derived and used to characterize the stability of equilibrium states. The analysis shows that the cancer-free equilibrium is globally stable when the threshold value remains below unity, while persistent tumor dynamics arise when it exceeds this critical level. Numerical simulations are carried out using the Atangana-Owolabi fractional numerical scheme and compared with fractional Adams-Bashforth and fractional Euler methods. Convergence analysis demonstrates improved numerical accuracy of the proposed approach. Computational experiments further reveal the influence of memory effects, immune clearance, and proliferation rates on tumor progression. The results highlight the importance of immune-mediated removal and targeted therapy in controlling malignant plasma cell populations and demonstrate the potential of fractional modeling for understanding complex tumor-immune-treatment interactions.